The Impact of Competing Time Delays in Coupled Stochastic Systems

TL;DR

This paper analyzes how different types of time delays affect synchronization in coupled stochastic systems, providing a scaling theory for phase boundaries and steady-state fluctuations, with implications for optimization.

Contribution

It introduces a scaling theory for the effects of competing transmission and processing delays on synchronization in stochastic systems.

Findings

Established the phase boundary for synchronization under delays

Derived asymptotic behavior near the boundary

Implications for optimizing delay trade-offs in synchronization

Abstract

We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays at each element. We establish the scaling theory for the phase boundary of synchronization and for the steady-state fluctuations in the synchronizable regime. Further, we provide the asymptotic behavior near the boundary of the synchronizable regime. Our results also imply the potential for optimization and trade-offs in synchronization problems with time delays.